

A202502


Modified lower triangular Fibonacci matrix, by antidiagonals.


2



1, 0, 2, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 3, 8, 0, 0, 0, 2, 5, 13, 0, 0, 0, 1, 3, 8, 21, 0, 0, 0, 0, 2, 5, 13, 34, 0, 0, 0, 0, 1, 3, 8, 21, 55, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55, 144, 0, 0, 0, 0, 0, 0, 2, 5, 13, 34, 89, 233, 0, 0, 0, 0, 0, 0, 1, 3, 8, 21, 55
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OFFSET

1,3


COMMENTS

This matrix, P, is used to form the Fibonacci selffission matrix as the product P*Q, where Q is the upper triangular Fibonacci matrix, A202451. To form P, delete the main diagonal of the transpose of Q.


LINKS

Table of n, a(n) for n=1..89.
Clark Kimberling, Fusion, Fission, and Factors, Fib. Q., 52 (2014), 195202.


EXAMPLE

Northwest corner:
1...0...0...0...0...0...0...0...0
2...1...0...0...0...0...0...0...0
3...2...1...0...0...0...0...0...0
5...3...2...1...1...0...0...0...0
8...5...3...2...1...1...0...0...0


MATHEMATICA

n = 14;
Q = NestList[Most[Prepend[#, 0]] &, #, Length[#]  1] &[Table[Fibonacci[k], {k, 1, n}]];
Qt = Transpose[Q]; P1 = Qt  IdentityMatrix[n];
P = P1[[Range[2, n], Range[1, n]]];
F = P.Q;
Flatten[Table[P[[i]][[k + 1  i]], {k, 1, n  1}, {i, 1, k}]] (* A202502 as a sequence *)
Flatten[Table[Q[[i]][[k + 1  i]], {k, 1, n  1}, {i, 1, k}]] (* A202451 as a sequence *)
Flatten[Table[F[[i]][[k + 1  i]], {k, 1, n  1}, {i, 1, k}]] (* A202503 as a sequence *)
TableForm[P] (* A202502, modified lower triangular Fibonacci matrix *)
TableForm[Q] (* A202451, upper tri. Fibonacci matrix *)
TableForm[F] (* A202503, Fibonacci selffission matrix *)


CROSSREFS

Cf. A202503, A202451, A202452, A202453, A000045.
Sequence in context: A062283 A136493 A132213 * A219839 A154312 A236076
Adjacent sequences: A202499 A202500 A202501 * A202503 A202504 A202505


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Dec 20 2011


STATUS

approved



